#### Algebraic and Geometric Topology 1 (2001),
paper no. 23, pages 445-468.

## On the linearity problem for mapping class groups

### Tara E. Brendle, Hessam Hamidi-Tehrani

**Abstract**.
Formanek and Procesi have demonstrated that Aut(F_n) is not linear for
n >2. Their technique is to construct nonlinear groups of a special
form, which we call FP-groups, and then to embed a special type of
automorphism group, which we call a poison group, in Aut(F_n), from
which they build an FP-group. We first prove that poison groups cannot
be embedded in certain mapping class groups. We then show that no
FP-groups of any form can be embedded in mapping class groups. Thus
the methods of Formanek and Procesi fail in the case of mapping class
groups, providing strong evidence that mapping class groups may in
fact be linear.
**Keywords**.
Mapping class group, linearity, poison group

**AMS subject classification**.
Primary: 57M07,20F65.
Secondary: 57N05,20F34.

**DOI:** 10.2140/agt.2001.1.445

**E-print:** `arXiv:math.GT/0103148`

Submitted: 24 March 2001.
(Revised: 17 August 2001.)
Accepted: 17 August 2001.
Published: 23 August 2001.

Notes on file formats
Tara E. Brendle, Hessam Hamidi-Tehrani

Columbia University

Department of Mathematics

New York, NY 10027, USA

B.C.C. of the City University of New York

Department of Mathematics and Computer Science

Bronx, NY 10453, USA

Email: tbrendle@math.columbia.edu, hessam@math.columbia.edu

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